{"paper":{"title":"On the boundedness of certain bilinear Fourier integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"David J. Rule, Salvador Rodriguez-Lopez, Wolfgang Staubach","submitted_at":"2011-11-20T17:39:56Z","abstract_excerpt":"We prove the global $L^2 \\times L^2 \\to L^1$ boundedness of bilinear Fourier integral operators with amplitudes in $S^0_{1,0} (n,2)$. To achieve this, we require that the phase function can be written as $(x,\\xi,\\eta) \\mapsto \\phase_1(x,\\xi) + \\phase_2(x,\\eta)$ where each $\\phase_j$ belongs to the class $\\Phi^2$ and satisfies the strong non-degeneracy condition. This result extends that of R. Coifman and Y. Meyer regarding pseudodifferential operators to the case of Fourier integral operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4653","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}